数学硕士论文代写-《有关数学向量均衡问题的探讨》
摘要 5-6
Abstract 6-7
第一章引言及预备知识 10-16
1.1引言 10-12
1.2预备知识 12-16
第二章向量均衡问题解的存在性与连通性 16-28
2.1不具有单调性的向量均衡问题 16-17
2.2具有伪单调性的向量均衡问题 17-22
2.3解的性质 22-24
2.4应用 24-28
2.4.1向量变分不等式的解 24-26
2.4.2向量优化问题的解 26-28
第三章参数向量均衡问题 28-36
3.1参数向量均衡问题及其特殊情形 28-29
3.2解的性质 29-33
3.3应用 33-36
第四章具有移动锥的参数向量均衡问题 36-44
4.1具有移动锥的参数向量均衡问题及其特殊情形 36-37
4.2解的性质 37-41
4.3应用 41-44
第五章结论 44-46
参考文献 46-48
致谢 48
【摘要】 均衡理论是数理经济的一个重要部分.自从Debreu证明了著名的均衡存在性定理之后,不少国内外学者对均衡理论这一课题进行了广泛的研究,并取得了许多优秀的成果,同时均衡理论的发展又促进了变分不等式理论、不动点理论、优化理论等数学研究领域的不断深入.均衡问题的解的存在性是均衡理论研究的中心问题.针对一般的均衡问题和向量均衡问题解的存在性,已有许多研究成果,受到这些成果的启发,本文主要从理论上较为系统的研究了一类向量均衡问题.1.对于向量均衡问题解的存在性,大多数学者通常是采用不动点定理、极大元定理等方法来进行研究,本文在不动点定理的基础上,引进了拓扑伪单调映射,然后利用拓扑伪单调的方法对具有伪单调性与没有单调性的向量均衡问题进行了深入研究,并引进了向量函数的(*)拟凹的概念,讨论了解的连通性.最后,作为应用,研究了向量变分不等式与向量优化问题解的存在性.2.利用通常的向量均衡问题解的存在性结果,通过引入适当的参数集合,得到了一类参数向量均衡问题,并用同样的方法证明了解的存在性以及解映射的连续性.作为应用,得到一类参数向量优化问题和参数向量变分不等式解映射的连续性.3.在某种凸性条件下,讨论了一类新的具有移动锥的参数向量均衡问题,利用参数向量均衡问题解的存在性结果,证明了解的存在性以及解映射的连续性,并得到一类广义参数向量优化问题和广义参数向量变分不等式解映射的连续性.
【Abstract】 Equilibrium theory is important in mathematical economics. Since the existence of equilibrium in an abstract economy which compact strategy set in Rn was proved in a seminal paper of Debreu, many famous scholars have studied it, and there have been many generalization of Debreu’s theorem. At the same time, the development of equilibrium theory stimulates the study of many fundamental mathematical fields such as variational inequality theory, optimization theory and the fixed point theory.The solution existence of equilibrium problems is the kernel of the study of the theory of equilibrium. According to the existence results of general equilibrium problems and vector equilibrium problems have been studied more and more. Inspired and motivated by these research results, this paper is devoted to study systematically a class of equilibrium problems.1. Many scholars usually utilize the maximal element theorems and the fixed point theorems to study existence of solutions for vector equilibrium problems. In this paper, topological pseudomonotone mapping is introduced and vector equilibrium problems of pseudomonotonicity and nonmontonicity are furtherly discussed on the basis of the fixed theorems. By using(*)-quasiconcavity of vector mappings, connectedness of solutions is presented. At last, we discuss the existence of solutions for vector variational inequalities and vector optimization problems to serve for application.2. According to the existence results of general equilibrium problems, a type of parametric vector equilibrium problem is obtained on the basis of some proper parametric set. The existence theorem and continuity properties of its solution mapping are proved in the same way. As its applications, the continuity of solution mappings for a class of parametric vector optimization problem and parametric vector variational inequality is obtained.3. A new type of parametric vector equilibrium problem with moving cones is introduced on the basis of some convexity and the existence theorem and continuity properties of its solution mapping are proved according to the existence results of parametric vector equilibrium problems. As its applications, the continuity of solution mappings for a class of generalized parametric vector optimization problems and parametric vector variational inequalilies is obtained.
硕士论文代写-【关键词】 向量均衡问题； 解映射； 连续性； 向量变分不等式； 向量优化问题；
【Key words】 vector equilibrium problem； solution mapping； continuity； vector variational inequality； vector optimization problem；//